Considering an area dodgy or safe is really a matter of perception.
Attacks on complete strangers are rare. Unless your son is involved in criminal activity and drugs, he will likely be safe wherever he lives.
Regardless of where he lives, he will presumably be going out late at night, going to different parts of London to see friends/do cultural things - he won't only be in whatever neighbourhood he buys in.
I wouldn't get hung up on him needing to live in a sleepy suburb to stay safe. The Mumsnet demographic is - naturally enough - going to suggest places more suitable for someone with young children than a 30 something single man who likes culture, socializing and going out.
Ex council is a solid choice - that was my first buy in Hackney ten years ago when 2 beds with private garden was 330k. I think a one bed without a garden still doable at that budget - the one on Old Roman Road looks interesting and lots of things to do around there, cool vibe etc.
People will wave their hands around and say they would never buy leasehold or ex council or whatever but that is because they are living different sorts of lives.
Or go for a studio - they are used to living in a room in shared house so they won't be used to masses of space
https://www.rightmove.co.uk/properties/142028639#/?channel=RES_BUY
Chatsworth Road is Hackney hipster central heaving with artisan bakeries, candle makers, craft beer etc. Mezzanine so feels more spacious that usual studio . 900 year lease.
https://www.rightmove.co.uk/properties/128386916#/?channel=RES_BUY
Decent studio in Fab building in great location Highgate, 90 year lease so at some point in the next 15 years he would prob need to pay to extend, just over budget but may be open to offers
Absolutely tiny studio but he is in a room already.. incredible location right near the Barbican so great for a culture vulture. doesn't say how long the lease is though. Service charge also not listed but given the building included a gym, swimming pool and communal laundry, it will be not low. However, amazing spot and no need for a gym membership elsewhere
https://www.rightmove.co.uk/properties/144310667#/?channel=RES_BUY